Essay - Mathematics George Cantor the Purpose of the Paper is to...

Mathematics

George Cantor

***** purpose of the paper is to develop a concept ***** the connection between mathematics and society from a his*****rical perspective. Specifically, it will discuss the subject, what George Cantor accomplished for mathematics and what that did for society. ***** Cantor's set theory changed the way mathematicians of the time looked at their science, and he revolutionized the way the world looks at numbers.

***** Cantor was a brilliant mathematician ***** philosopher who developed the modern mathematical idea of infinity, along with the idea ***** an infinite set of real numbers, called transfinite sets, or ***** "set the*****y." In addition, Cantor found that real numbers were not countable, while algebraic numbers were countable (Breen). ***** views were quite controversial when he first developed them in the late 1800s, and some mathematicians today question some of his hypothesis ("Transf*****ite Number"), however, his work is recognized as some ***** the most important ***** thought of our time. Not only ***** Cantor get other ***** thinking about problems ***** had plagued them for years, he changed the way they looked at ***** in general - it made ***** question what numbers actually are.

***** did Cantor's theories affect society? ***** work, which he attributed to God's divine wisdom showing him the solutions, changed the way mathematicians looked at their work. It also stirred up interest in ***** that ***** waned dur*****g the Victorian era. Even more importantly, ***** theories spilled over into many other innovations of the day, including the atomistic statistical *****rmodynamics, stop-motion photography, ***** even the color-plane type ***** painting by Gauguin and Bernard (Everdell 46). ***** addition, Cantor's *****s ***** inspired philosophical thought in any number of his contemporaries, because ma*****maticians like Bertrand Russell and Ludwig Wittgenstein turned to philosophical ***** to explain and even try to disprove Cantor's theories. Cantor's set theories ***** *****s to create, think, prove, and disprove, and so, his work ***** only created a ***** underst*****ndable and workable form of arithmetic, it created new thought and new art forms that changed ********** ***** how society looked at science. When people began to understand that mathematics could influence everything from pho*****graphy to art and science, they took a greater interest in mathematics and philosophical thought, ***** ***** turn led to even more innovation ***** scientific *****. In fact, to*****, m***** scientists and mathematicians feel Cantor's work represented a real paradigm shift, or a r*****dical change in mathematical and philosophical ***** ("Cantor"). Two ***** his l*****ting models ***** s*****ed his theories ***** "***** Comb," which showed all points were disconnected from each other, and "Cantor's Dust," which calls these ***** sets "fractal dust" (Breen). Cantor's work really ***** mathematics, and encouraged people to think *****ly about just ***** numbers really were.

*****, Cantor's mental health deteriorated as he aged, ***** he had sev*****l nervous breakdowns in reaction to criticism of his work. Today, many believe he suffered from bipolar disorder ("Can*****r"). It is sad to think that Cantor may have contributed ***** more to